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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.credits"></a><a class="link" href="credits.html" title="Credits and Acknowledgements">Credits and Acknowledgements</a>
</h2></div></div></div>
<div class="note"><table border="0" summary="Note">
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<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/src/images/note.png"></td>
<th align="left">Note</th>
</tr>
<tr><td align="left" valign="top"><p>
        This section should be read with the 'What's New' section that gives much
        detail on changes for each release.
      </p></td></tr>
</table></div>
<p>
      Hubert Holin started the Boost.Math library. The Quaternions, Octonions, inverse
      hyperbolic functions, and the sinus cardinal functions are his.
    </p>
<p>
      Daryle Walker wrote the integer gcd and lcm functions.
    </p>
<p>
      John Maddock started the special functions, the beta, gamma, erf, polynomial,
      and factorial functions are his, as is the "Toolkit" section, and
      many of the statistical distributions.
    </p>
<p>
      Paul A. Bristow threw down the challenge in <a href="http://www2.open-std.org/JTC1/SC22/WG21/docs/papers/2004/n1668.pdf" target="_top">A
      Proposal to add Mathematical Functions for Statistics to the C++ Standard Library</a>
      to add the key math functions, especially those essential for statistics. After
      JM accepted and solved the difficult problems, not only numerically, but in
      full C++ template style, PAB implemented a few of the statistical distributions.
      PAB also tirelessly proof-read everything that JM threw at him (so that all
      remaining editorial mistakes are his fault).
    </p>
<p>
      Xiaogang Zhang worked on the Bessel functions and elliptic integrals for his
      Google Summer of Code project 2006.
    </p>
<p>
      Bruno Lalande submitted the "compile time power of a runtime base"
      code.
    </p>
<p>
      Johan Råde wrote the optimised floating-point classification and manipulation
      code, and nonfinite facets to permit C99 output of infinities and NaNs. (nonfinite
      facets were not added until Boost 1.47 but had been in use with Boost.Spirit).
      This library was based on a suggestion from Robert Ramey, author of Boost.Serialization.
      Paul A. Bristow expressed the need for better handling of <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2006/n2022.pdf" target="_top">Input
      &amp; Output of NaN and infinity for the C++ Standard Library</a> and suggested
      following the C99 format.
    </p>
<p>
      Antony Polukhin improved lexical cast avoiding stringstream so that it was
      no longer necessary to use a globale C99 facet to handle nonfinites.
    </p>
<p>
      Håkan Ardö, Boris Gubenko, John Maddock, Markus Schöpflin and Olivier Verdier
      tested the floating-point library and Martin Bonner, Peter Dimov and John Maddock
      provided valuable advice.
    </p>
<p>
      Gautam Sewani coded the logistic distribution as part of a Google Summer of
      Code project 2008.
    </p>
<p>
      M. A. (Thijs) van den Berg coded the Laplace distribution. (Thijs has also
      threatened to implement some multivariate distributions).
    </p>
<p>
      Thomas Mang requested the inverse gamma in chi squared distributions for Bayesian
      applications and helped in their implementation, and provided a nice example
      of their use.
    </p>
<p>
      Professor Nico Temme for advice on the inverse incomplete beta function.
    </p>
<p>
      <a href="http://www.shoup.net" target="_top">Victor Shoup for NTL</a>, without which
      it would have much more difficult to produce high accuracy constants, and especially
      the tables of accurate values for testing.
    </p>
<p>
      We are grateful to Joel Guzman for helping us stress-test his <a href="http://www.boost.org/tools/quickbook/index.htm" target="_top">Boost.Quickbook</a>
      program used to generate the html and pdf versions of this document, adding
      several new features en route.
    </p>
<p>
      Plots of the functions and distributions were prepared in <a href="http://www.w3.org/" target="_top">W3C</a>
      standard <a href="http://www.svg.org/" target="_top">Scalable Vector Graphic (SVG)</a>
      format using a program created by Jacob Voytko during a <a href="http://code.google.com/soc/2007/" target="_top">Google
      Summer of Code (2007)</a>. From 2012, the latest versions of all Internet
      Browsers have support for rendering SVG (with varying quality). Older versions,
      especially (Microsoft Internet Explorer (before IE 9) lack native SVG support
      but can be made to work with <a href="http://www.adobe.com/svg/viewer/install/" target="_top">Adobe's
      free SVG viewer</a> plugin). The SVG files can be converted to JPEG or
      PNG using <a href="http://www.inkscape.org/" target="_top">Inkscape</a>.
    </p>
<p>
      We are also indebted to Matthias Schabel for managing the formal Boost-review
      of this library, and to all the reviewers - including Guillaume Melquiond,
      Arnaldur Gylfason, John Phillips, Stephan Tolksdorf and Jeff Garland - for
      their many helpful comments.
    </p>
<p>
      Thanks to Mark Coleman and Georgi Boshnakov for spot test values from <a href="http://www.wolfram.com/products/mathematica/index.html" target="_top">Wolfram Mathematica</a>,
      and of course, to Eric Weisstein for nurturing <a href="http://mathworld.wolfram.com" target="_top">Wolfram
      MathWorld</a>, an invaluable resource.
    </p>
<p>
      The Skew-normal distribution and Owen's t function were written by Benjamin
      Sobotta.
    </p>
<p>
      We thank Thomas Mang for persuading us to allow t distributions to have infinite
      degrees of freedom and contributing to some long discussions about how to improve
      accuracy for large non-centrality and/or large degrees of freedom.
    </p>
<p>
      Christopher Kormanyos wrote the e_float multiprecision library <a href="http://portal.acm.org/citation.cfm?id=1916469" target="_top">TOMS
      Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function
      Calculations</a> which formed the basis for the Boost.Multiprecision library
      which now can be used to allow most functions and distributions to be computed
      up to a precision of the users' choice, no longer restricted to built-in floating-point
      types like double. (And thanks to Topher Cooper for bring Christopher's e_float
      to our attention).
    </p>
<p>
      Christopher Kormanyos wrote some examples for using <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>,
      and added methods for finding zeros of Bessel Functions.
    </p>
<p>
      Marco Guazzone provided the hyper-geometric distribution.
    </p>
<p>
      Rocco Romeo has found numerous small bugs and generally stress tested the special
      functions code to near destruction!
    </p>
<p>
      Jeremy William Murphy added polynomial arithmetic tools.
    </p>
<p>
      Thomas Luu provided improvements to the quantile of the non-central chi squared
      distribution quantile. and his thesis * <a href="http://discovery.ucl.ac.uk/1482128/" target="_top">Fast
      and accurate parallel computation of quantile functions for random number generation,
      2016</a>.
    </p>
<p>
      and his paper
    </p>
<p>
      Luu, Thomas; (2015), Efficient and Accurate Parallel Inversion of the Gamma
      Distribution, SIAM Journal on Scientific Computing , 37 (1) C122 - C141, <a href="https://doi.org/10.1137/14095875X" target="_top">https://doi.org/10.1137/14095875X</a>.
    </p>
<p>
      These also promise to help improve algorithms for computation of quantile of
      several distributions, especially for parallel computation using GPUs.
    </p>
<p>
      Nicolas Thompson added much code to handle quadrature and interpolation and
      more statistical tools.
    </p>
<p>
      Matthew Pulver provided the automatic differentiation section for inclusion
      in Boost.Math.
    </p>
</div>
<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
      Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
      Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
      Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
      Walker and Xiaogang Zhang<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
      </p>
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